QUESTION TYPE: Must be True
- Pet store (Most)➞ has birds
- Has birds (Most) ➞ Has fish
- Fish and
Gerbils➞ NOT(Fish and Birds)
ANALYSIS: First, you can’t combine “most” statements with anything. You can only combine “most” statements with the sufficient condition of a conditional statement.
Second, let’s talk about contrapositives. Normally, you would draw a contrapositive by negating both statements, and changing “and” to “or”, like this:
Gerbils ➞ Fish or Birds
You probably drew that, but still struggled. The diagramming method above is just a trick to get you to the right place. But it’s better to know what a contrapositive really is.
Contrapositives are really just “not that”, whatever that is. The negation of something is just “not that thing”. This gets complicated with compound conditions (e.g. this AND that). There are four possibilities with any compound statement. Let’s use tropical fish and exotic birds as an example:
- Fish and birds
- Fish and
birds Fishand birds
The sufficient condition in the stimulus is the third one. So the contrapositive is “not the third one”. So numbers 1, 2 and 4 are all included in the contrapositive.
Birds)” capture this idea better than “ Fish or Birds”. Both statements actually mean “any of 1, 2 or 4”, but the first one is much clearer. And the correct answer, D, is phrased in the form of “NOT(Fish and Birds)”.
- We only know that independently owned pet stores don’t sell gerbils. This answer says “most”. The fact about gerbils doesn’t connect with any “most” statements.
- We only know that no independently owned pet stores sell gerbils. This answer talks about all pet stores. The bird and fish part is wrong too: it should have said “no pet stores….sell tropical fish but not exotic birds”. That’s what we can conclude about a pet store that doesn’t sell gerbils.
- We don’t even know if any independently owned pet stores do sell gerbils. The question gives us a sufficient condition for a store to sell gerbils, but it doesn’t tell us whether any pet stores do meet that sufficient condition.
- CORRECT. This is the contrapositive of the conditional statement from the stimulus. If a pet store “sells tropical fish but not exotic birds” then it sell gerbils.
So if a pet store doesn’t sell gerbils, then it doesn’t “sell tropical fish and not exotic birds”.
Note: And = But
See the analysis section above for more detail.
- We have no idea. We know that independent pet stores don’t sell gerbils. That just means they can’t “sell tropical fish but not exotic birds”.
As long as they don’t do that, they could sell:
1. Tropical fish and exotic birds
2. No tropical fish and no exotic birds
3. No tropical fish, and exotic birds
This answer is too restricted. It excludes the third possibility.
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